Integral graphs obtained by dual Seidel switching

Dual Seidel switching is a graph operation introduced by W. Haemers in 1984. This operation can change the graph, however it does not change its bipartite double, and because of this, the operation leaves the squares of the eigenvalues invariant. Thus, if a graph is integral then it is still integra...

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Bibliographic Details
Published in:Linear algebra and its applications 2020-11, Vol.604, p.476-489
Main Authors: Goryainov, Sergey, Konstantinova, Elena V., Li, Honghai, Zhao, Da
Format: Article
Language:English
Subjects:
4-Regular graph
Dual Seidel switching
Eigenvalues
Graphs
Integral graph
Integrals
Linear algebra
Multiple Kronecker covering
Odd graph
Star graph
Switching
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Summary:Dual Seidel switching is a graph operation introduced by W. Haemers in 1984. This operation can change the graph, however it does not change its bipartite double, and because of this, the operation leaves the squares of the eigenvalues invariant. Thus, if a graph is integral then it is still integral after dual Seidel switching. In this paper two new infinite families of integral graphs are obtained by applying dual Seidel switching to the Star graphs and the Odd graphs. In particular, three new 4-regular integral graphs with their spectra are found.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.07.010